Critical analysis of modulus stabilization in a higher dimensional F (R ) gravity

An exact solution for the bulk five-dimensional geometry is derived for F (R ) gravity with nonflat de Sitter 3-branes located at the M₄×Z₂ orbifold boundaries. The corresponding form of F (R ) that leads to such an exact solution of the bulk metric is derived, which turns out to have all positive integer powers of R . In such a scenario, the stability issue of the modulus (radion field) is analyzed critically for different curvature epochs in both Einstein and Jordan frames. The radion in the effective 4D theory exhibits a phantom epoch, making this model viable for a nonsingular bounce. Simultaneous resolution of the gauge-hierarchy problem is exhibited through the resulting stable value of the radion field in the effective 3 +1 -dimensional theory.